Chapter One Crystal Structure
|
|
- Brittney Higgins
- 6 years ago
- Views:
Transcription
1 Chpter One Crystl Structure Drusy Qurtz in Geode Tbulr Orthoclse Feldspr Encrusting Smithsonite Peruvin Pyrite 1
2 Snow crystls the Beltsville Agriculturl Reserch Center
3 Solid : Crystl vs. Amorphous (glssy) Ordered rry of toms Disordered rrngement Competition between ttrctive (binding) force nd repulsive force. Regulr rry lowers system energy. Complicted! -- difficult to predict the structure of mterils 3
4 Importnce : structure plys mjor role in determining physicl properties of solids Determintion : X-ry nd neutron scttering re key tools for determining crystl structures. (bulk) Also microscopic techniques such s SEM, TEM, STM, AFM (surfce) Devitions : There is no perfect crystl. Mny key properties depend on devition more. Defects imperfection in crystl Phonons lttice vibrtions 4
5 Clcite(CCO 3 ) crystl is mde from sphericl prticles. Christin Huygen, Leiden 1690 A crystl is mde from sphericl prticles. Robert Hooke, London 1745 depicted by René Hüy, Pris, 18 5
6 Crystl periodic rry of toms : point lttice + bsis Point lttice mthemticl points in spce r = u 1 1,u, r +, u, u u integer = + + u 3 lttice vectors 3 r r 1 6
7 Primitive lttice cell A cell will fill ll spce by the repetition of suitble crystl trnsltion opertions A minimum volume cell. A.One lttice point per primitive cell..the bsis ssocited w/. primitive cell -- primitive bsis.not unique. cell r = r = 1 1 r r sinφ Sme for ll primitive cells Uniform mss density Dimensions r r 1 Wigner-Seitz Primitive cell -- lttice point is t its center the highest symmetry cell possible 7
8 Wigner-Seitz Primitive cell in D (or 3D) Drw lines to connect given lttice point to ll nerby lttice points.. Drw bisecting lines (or plnes) to the previous lines.. The smllest re (or volume) enclosed. D Oblique Lttice 8
9 Fundmentl types of Brvis lttices Bsed on symmetries : 1) Trnsltionl sme if trnslte by vector T = u u u3 3 ) Rottionl sme if lttice is rotted by n ngle bout point -fold by 180 o 4-fold by 90 o 3-fold by 10 o 6-fold by 60 o 3) Mirror symmetry sme if reflected bout plne Auguste Brvis 4) Inversion symmetry sme if reflected through point (equivlent to rottion 180 o nd mirror rottionl xis r -r 9
10 Five Brvis lttices in two dimensions Squre lttice 1 =, φ=90 o Unit cell Symmetry element r φ r 1 Rectngulr lttice 1, φ=90 o Symmetry Unit cell element 10
11 Oblique lttice 1, φ 60 o, 90 o Symmetry Unit cell element Centered Rectngulr lttice r r 1 φ 1 = cosφ Unit cell Symmetry element 11
12 Hexgonl lttice 1 =, φ=60 o Symmetry element Unit cell twofold xis (di) threefold xis (trid) fourfold xis (tetrd) sixfold xis (hexd) mirror line 1
13 A Brvis lttice is lttice in which every lttice point hs exctly the sme environment. How bout honeycomb lttice? A honeycomb crystl = A hexgonl lttice + two-pint bsis 13
14 System Triclinic Monoclinic The seven crystl systems divided into fourteen Brvis lttices : Number of lttices 1: Simple Simple, Bse-Centered Unit cell chrcteristics 1 3 α β γ 1 3 α = β = 90 o γ Chrcteristic symmetry elements None One -fold rottion xis Orthorhombic 4: BCC, FCC Simple, Bse-Centered 1 3 α = β = γ = 90 o Three mutully orthogonl -fold rottion xes Tetrgonl : Simple, BCC 1 = 3 α = β = γ = 90 o One 4-fold rottion xis Cubic 3: Simple, BCC, FCC 1 = = 3 α = β = γ = 90 o Four 3-fold rottion xes Trigonl 1: Simple 1 = = 3 α = β = γ<10 o 90 o One 3-fold rottion xis Hexgonl 1: Simple 1 = 3 α = β = 90 o, γ =10 o One 3-fold rottion xis 14
15 TRICLINIC (α β γ) MONOCLINIC (β=γ=90 o α) 1 β γ α 3 Simple 1 Simple Bse-centered 15
16 Orthorhombic (α=β=γ=90 o ) 1 3 β 1 3 α γ Simple Bse-centered BCC FCC 16
17 Tetrgonl (α=β=γ=90 o ) 1 β α γ 1 Simple BCC 17
18 Cubic (α=β=γ=90 o ) β α γ Simple BCC FCC 18
19 Trigonl (α=β=γ<10 o, 90 o ) Hexgonl (α=β=90 o, γ=10 o ) 3 3 γ=10 o Simple Simple 19
20 Chrcteristics of cubic lttices Simple Body-centered Fce-centered Lttice points/cell 1 4 Number of nerest neighbors Nerest- neighbor distnce Pcking frction π 6 = π = π = Mximum, sme s hexgonl 0
21 Crystl Periodic rrngement of toms Brvis lttice + Bsis of tom (Arry of point in spce) (Arrngement of toms within unit cell) Dimensions 5 types 3 Dimensions 14 types By symmetry Crystl my hve sme or less symmetry thn originl Brvis lttice. Bsis Symmetry 4mm 1
22 Introducing new symmetries for bsis with multiple toms : Point group symmetries : combintions of rottion, inversion, reflection tht hold one point fixed nd return originl structure. Dimensions, 10 3 Dimensions, 3 Spce group symmetries : point group opertions + trnsltions tht return originl structure. Dimensions, 17 3 Dimensions, 30 There re mny possible types by symmetry but most re never observed. Rel crystls form few types due to energies of crystl formtion.
23 3
24 Directions nd plnes in crystls Useful to develop nottion for describing directions nd identifying plnes of toms in crystls r = u + Consider lttice defined by 1,, u u3 3 Vector direction is described s [u 1 u u 3 ] Note : where u 1, u, nd u 3 re the lowest reduced integers. [8 6 0] sme s [4 3 0] use ū insted of -u [11] [u 1 u u 3 ] not s the sme s Crtesin coordinte direction except for simple cubic crystl 4
25 Cubic hs highest symmetric directions [ ] [ ] [ ] [ ] [ ] By symmetry, [ ], [ ], [ ] re equivlent [ ],[ ],[ ] Denote { } set of equivlent directions 5
26 Crystl plnes toms fll on plnes lbeled by Miller indices Note : Find the intercepts on the xes in terms of 1,, nd 3 h k l Tke reciprocls nd mke integers ( ) h' k ' l' h' k' l' Reduce to smllest three integers If the plne does not intersect one of the crystl xes, tht intercept is tken to be infinitely fr from the origin nd the corresponding index is zero. ( h k l ) is clled Miller index of the plne Miller indices specify vector norml to the plne, nd not specific plne : ll prllel plnes hve the sme indices 6
27 Schemtic illustrtions of lttice plnes Lines in two dimensionl crystls r r 1 (11) (01) (5) Low index plne : more dense nd more widely spced High index plne : Less dense nd more closely spced 7
28 Most common crystl structures : Simple Cubic lttice : Po conventionl cell : 1 tom/cube Body Centered Cubic lttice : Conventionl cell : toms/ cube Not primitive lttice (1/,1/,1/) 8 nerest neighbors (0,0,0) Alkli metls : Li, N, K, Rb, Cs Ferromgnetic metls : Cr, Fe Trnsition metls : Nb, V, T, Mo, W BCC lttice + single tom bsis SC lttice + bsis of toms t (0,0,0) nd (1/,1/,1/) 8
29 Body Centered Cubic lttice x 3 z 1 y 1 3 = (xˆ + ŷ ẑ) = ( xˆ + ŷ + ẑ) = (xˆ ŷ + ẑ) 9
30 Body-centered Cubic lttice Primitive cell : Rhombohedron w/ edge. the ngle between two djcent edges is 109 o 8 30
31 Fce Centered Cubic lttice : Conventionl cell : 4 toms/ cube Not primitive lttice (1/,0,1/) (0,1/,1/) 1 nerest neighbors (0,0,0) (1/,1/,0) Noble metls : Cu, Ag, Au Trnsition metls : Ni, Pd, Pt, Inert gs solids : Ne, Ar, Kr, Xe FCC lttice + single tom bsis SC lttice + bsis of 4 toms t (0,0,0), (1/,1/,0) (1/,0,1/), nd (0,1/,1/) 31
32 Fce Centered Cubic lttice x 3 z 1 y 1 3 = = = (xˆ + (ŷ + (xˆ + ŷ) ẑ) ẑ) Rhombohedrl Primitive cell The ngle between two djcent edges : 60 o Edge 3
33 Hexgonl Close-Pcked lttice c 3 c 1 =, = with n included ngle10 1 1,, nd c do not construct primitive lttice 1,, nd 3 construct primitive lttice 1 nerest neighbors 1 = = 3 o 1 Trnsition metls : Sc, Y, Ti, Zr, Co IIA metls : Be, Mg Bsl Plne Hexgonl lttice + bsis of toms t (0,0,0) nd (/3,1/3,1/) 33
34 HCP lttice A B A B A B z y x FCC lttice A B C A B C A B C 34
35 Dimond structure : two FCC displced from ech other by ¼ of body digonl FCC lttice + bsis of toms t (0,0,0) nd (1/4,1/4,1/4) 0 1/ 0 3/4 1/4 1/ 0 1/ 1/4 3/4 0 1/ 0 Tetrhedrl bonding : 4 nerest neighbors 1 next nerest neighbors The mximum pcking frction = 0.34 Si, Ge, Sn, C, ZnS, GAs, 35
36 Some toms form multiple stble structures: for exmple, C dimond or grphite (hexgonl) An STM imge of grphite surfce clerly shows the interconnected 6-membered rings of grphite 36
37 grphite dimond 37
38 Mny crystls undergo structurl chnges with T, P: for exmple, Fe δ-ferrite α-ferrite BCC FCC BCC Liquid 910 o C 1400 o C 100 o C Temperture N HCP 36K FCC 371K Liquid Temperture 38
39 Compounds NCl structures NCl, NF, KCl, AgCl, MgO, MnO, FCC lttice + bsis of two toms Cl (0,0,0), N (1/,1/,1/) SC w/. lternting toms CsCl structures CsCl, BeCu, ZnCu(brss), AlNi, AgMg, SC lttice + bsis of two toms Cs (0,0,0), Cl (1/,1/,1/) BCC w/. lternting toms 39
40 ZnS structures Znicblende ZnS, CuF, CuCl, CdS GAs, GP, InSb, compounds Photoconductor III-V semiconducting compounds FCC lttice + bsis of two toms Zn (0,0,0), S (1/4,1/4,1/4) G(0,0,0), As(1/4,1/4,1/4) dimond w/. lternting toms 40
41 41
42 High Tc superconductors c b O(4) Pr Pr Pr Cu() O() Cu() O() Cu() O() O(1) B/Pr O(1) B/Pr O(1) B/Pr Cu(1) O(3) O(5) Cu(1) O(3) Cu(1) O(3) Orthorhombic O(I) (Pmmm) Tetrgonl T (P4/mmm) Orthorhombic O(II) (Cmmm) 4
43 C-60 Bucky blls BuckminsterFullurene 43
STRUCTURAL ISSUES IN SEMICONDUCTORS
Chpter 1 STRUCTURAL ISSUES IN SEMICONDUCTORS Most semiconductor devices re mde from crystlline mterils. The following gures provide n overview of importnt crystlline properties of semiconductors, like
More informationAnalytical Methods for Materials
Anlyticl Methods for Mterils Lesson 7 Crystl Geometry nd Crystllogrphy, Prt 1 Suggested Reding Chpters 2 nd 6 in Wsed et l. 169 Slt crystls N Cl http://helthfreedoms.org/2009/05/24/tble-slt-vs-unrefined-se-slt--primer/
More informationQUB XRD Course. The crystalline state. The Crystalline State
QUB XRD Course Introduction to Crystllogrphy 1 The crystlline stte Mtter Gseous Stte Solid stte Liquid Stte Amorphous (disordered) Crystlline (ordered) 2 The Crystlline Stte A crystl is constructed by
More information1.Bravais Lattices The Bravais lattices Bravais Lattice detail
1.Brvis Lttices 12.1. The Brvis lttices 2.2.4 Brvis Lttice detil The Brvis lttice re the distinct lttice types which when repeted cn fill the whole spce. The lttice cn therefore be generted by three unit
More informationCrystalline Structures The Basics
Crystlline Structures The sics Crystl structure of mteril is wy in which toms, ions, molecules re sptilly rrnged in 3-D spce. Crystl structure = lttice (unit cell geometry) + bsis (tom, ion, or molecule
More informationSolid State Electronics EC210 Arab Academy for Science and Technology AAST Cairo Spring 2016 Lecture 1 Crystal Structure
Solid Stte Electronics EC210 AAST Ciro Spring 2016 Lecture 1 Crystl Structure Dr. Amr Byoumi, Dr. Ndi Rft 1 These PowerPoint color digrms cn only be used by instructors if the 3 rd Edition hs been dopted
More informationLUMS School of Science and Engineering
LUMS School of Science nd Engineering PH- Solution of ssignment Mrch, 0, 0 Brvis Lttice Answer: We hve given tht c.5(î + ĵ + ˆk) 5 (î + ĵ + ˆk) 0 (î + ĵ + ˆk) c (î + ĵ + ˆk) î + ĵ + ˆk + b + c î, b ĵ nd
More informationWhat is solid state physics?
Wht is solid stte physics? Explins the properties of solid mterils. Explins the properties of collection of tomic nuclei nd electrons intercting with electrosttic forces. Formultes fundmentl lws tht govern
More informationfiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics
Solid Stte Physics JEST-0 Q. bem of X-rys is incident on BCC crystl. If the difference between the incident nd scttered wvevectors is K nxˆkyˆlzˆ where xˆ, yˆ, zˆ re the unit vectors of the ssocited cubic
More informationIV. CONDENSED MATTER PHYSICS
IV. CONDENSED MATTER PHYSICS UNIT I CRYSTAL PHYSICS Lecture - II Dr. T. J. Shinde Deprtment of Physics Smt. K. R. P. Kny Mhvidyly, Islmpur Simple Crystl Structures Simple cubic (SC) Fce centered cubic
More informationMiller indices and Family of the Planes
SOLID4 Miller Indices ltest Fmily of Plnes nd Miller indices; Miller indices nd Fmily of the Plnes The geometricl fetures of the crystls represented by lttice points re clled Rtionl. Thus lttice point
More informationPoint Lattices: Bravais Lattices
Physics for Solid Stte Applictions Februry 18, 2004 Lecture 7: Periodic Structures (cont.) Outline Review 2D & 3D Periodic Crystl Structures: Mthemtics X-Ry Diffrction: Observing Reciprocl Spce Point Lttices:
More informationLecture V. Introduction to Space Groups Charles H. Lake
Lecture V. Introduction to Spce Groups 2003. Chrles H. Lke Outline:. Introduction B. Trnsltionl symmetry C. Nomenclture nd symols used with spce groups D. The spce groups E. Derivtion nd discussion of
More information1 1. Crystallography 1.1 Introduction 1.2 Crystalline and Non-crystalline materials crystalline materials single crystals polycrystalline material
P g e. Crystllogrphy. Introduction Crystllogrphy is the brnch of science tht dels bout the crystl structures of elements. The crystl structures of elements re studied by mens of X-ry diffrction or electron
More information2010. Spring: Electro-Optics (Prof. Sin-Doo Lee, Rm ,
2010. Spring: Electro-Optics (Prof. Sin-Doo Lee, Rm. 301-1109, http://mipd.snu.c.kr) Opticl Wves in Crystls A. Yriv nd P. Yeh (John Wiley, New Jersey, 2003) Week Chpter Week Chpter Mr. 03 * Bsics of Crystl
More informationPHY 140A: Solid State Physics. Solution to Midterm #1
PHY 140A: Solid Stte Physics Solution to Midterm #1 TA: Xun Ji 1 October 24, 2006 1 Emil: jixun@physics.ucl.edu Problem #1 (20pt)Clculte the pcking frction of the body-centered cubic lttice. Solution:
More informationChapter 3: The Structure of Crystalline Solids (2)
Chpter 3: The Structure of Crstlline Solids (2) Clss Eercise Drw the unit cell structure for simple cubic (SC), bodcentered cubic (BCC), nd fce-centered cubic (FCC) lttices Give coordintion number (CN)
More informationB M S INSTITUTE OF TECHNOLOGY [Approved by AICTE NEW DELHI, Affiliated to VTU BELGAUM] DEPARTMENT OF PHYSICS. Crystal Structure
B M S INSTITUTE OF TECHNOLOGY [Approved by AICTE NEW DELHI, Affilited to VTU BELGAUM] DEPARTMENT OF PHYSICS COURSE MATERIAL SUBJECT: - Engineering Physics MODULE -IV SUBJECT CODE: - 14 PHY 1 / Crystl Structure
More informationDETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE
Determintion RevAdvMterSci of mechnicl 0(009) -7 properties of nnostructures with complex crystl lttice using DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING
More informationCrystals Statics. Structural Properties. Geometry of lattices. Aug 23, 2018
Crystals Statics. Structural Properties. Geometry of lattices Aug 23, 2018 Crystals Why (among all condensed phases - liquids, gases) look at crystals? We can take advantage of the translational symmetry,
More informationKai Sun. University of Michigan, Ann Arbor
Ki Sun University of Michign, Ann Arbor How to see toms in solid? For conductors, we cn utilize scnning tunneling microscope (STM) to see toms (Nobel Prize in Physics in 1986) Limittions: (1) conductors
More informationCrystals. Fig From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005)
Crystls Mterils will often orgnize themselves by minimizing energy to hve long rnge order. This order results in periodicity tht determines mny properties of the mteril. We represent this periodicity by
More informationChapter 2: Crystal Structures and Symmetry
hpter 2: rystl Structures nd Symmetry Lue, rvis Jnury 30, 2017 ontents 1 Lttice Types nd Symmetry 3 1.1 Two-Dimensionl Lttices................. 3 1.2 Three-Dimensionl Lttices................ 5 2 Point-Group
More informationChapter 16. Molecular Symmetry
I. Smmetr Chpter 6. Moleculr Smmetr Elements xis mirror plne inversion center... Opertions rottion bout n xis reflection thru plne inversion thru center Five smmetr elements nd corresponding opertions:
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More informationLecture 6 - Bonding in Crystals
Lecture 6 onding in Crystals inding in Crystals (Kittel Ch. 3) inding of atoms to form crystals A crystal is a repeated array of atoms Why do they form? What are characteristic bonding mechanisms? How
More informationR. I. Badran Solid State Physics
I Bdrn Solid Stte Physics Crystl vibrtions nd the clssicl theory: The ssmption will be mde to consider tht the men eqilibrim position of ech ion is t Brvis lttice site The ions oscillte bot this men position
More informationPhys 412 Solid State Physics. Lecturer: Réka Albert
Phys 412 Solid State Physics Lecturer: Réka Albert What is a solid? A material that keeps its shape Can be deformed by stress Returns to original shape if it is not strained too much Solid structure
More informationDEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS
3 DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS This chpter summrizes few properties of Cli ord Algebr nd describe its usefulness in e ecting vector rottions. 3.1 De nition of Associtive
More informationPART 1 Introduction to Theory of Solids
Elsevier UK Job code: MIOC Ch01-I044647 9-3-2007 3:03p.m. Page:1 Trim:165 240MM TS: Integra, India PART 1 Introduction to Theory of Solids Elsevier UK Job code: MIOC Ch01-I044647 9-3-2007 3:03p.m. Page:2
More informationORBITAL DIAGRAM - A graphical representation of the quantum number "map" of electrons around an atom.
178 (MAGNETIC) SPIN QUANTUM NUMBER: "spin down" or "spin up" - An ORBITAL (region with fixed "n", "l" and "ml" values) can hold TWO electrons. ORBITAL DIAGRAM - A graphical representation of the quantum
More informationAnalytically, vectors will be represented by lowercase bold-face Latin letters, e.g. a, r, q.
1.1 Vector Alger 1.1.1 Sclrs A physicl quntity which is completely descried y single rel numer is clled sclr. Physiclly, it is something which hs mgnitude, nd is completely descried y this mgnitude. Exmples
More informationExam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B
PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere
More informationa * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2
18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions
More informationCHEMICAL COMPOUNDS MOLECULAR COMPOUNDS
48 CHEMICAL COMPOUNDS - Dalton's theory does not mention this, but there is more than one way for atoms to come together to make chemical compounds! - There are TWO common kinds of chemical compound, classified
More informationENERGY AND PACKING. Outline: MATERIALS AND PACKING. Crystal Structure
EERGY AD PACKIG Outline: Crstlline versus morphous strutures Crstl struture - Unit ell - Coordintion numer - Atomi pking ftor Crstl sstems on dense, rndom pking Dense, regulr pking tpil neighor ond energ
More information2 Calculate the size of each angle marked by a letter in these triangles.
Cmridge Essentils Mthemtics Support 8 GM1.1 GM1.1 1 Clculte the size of ech ngle mrked y letter. c 2 Clculte the size of ech ngle mrked y letter in these tringles. c d 3 Clculte the size of ech ngle mrked
More informationCHEMICAL COMPOUNDS MOLECULAR COMPOUNDS
48 CHEMICAL COMPOUNDS - Dalton's theory does not mention this, but there is more than one way for atoms to come together to make chemical compounds! - There are TWO common kinds of chemical compound, classified
More information-"l" also contributes ENERGY. Higher values for "l" mean the electron has higher energy.
175 - Giving the four parameters will uniquely identify an electron around an atom. No two electrons in the same atom can share all four. These parameters are called QUANTUM NUMBERS. PRINCIPAL QUANTUM
More informationLevel I MAML Olympiad 2001 Page 1 of 6 (A) 90 (B) 92 (C) 94 (D) 96 (E) 98 (A) 48 (B) 54 (C) 60 (D) 66 (E) 72 (A) 9 (B) 13 (C) 17 (D) 25 (E) 38
Level I MAML Olympid 00 Pge of 6. Si students in smll clss took n em on the scheduled dte. The verge of their grdes ws 75. The seventh student in the clss ws ill tht dy nd took the em lte. When her score
More informationCh. 9 NOTES ~ Chemical Bonding NOTE: Vocabulary terms are in boldface and underlined. Supporting details are in italics.
Ch. 9 NOTES ~ Chemical Bonding NOTE: Vocabulary terms are in boldface and underlined. Supporting details are in italics. I. Review: Comparison of ionic and molecular compounds Molecular compounds Ionic
More informationIntroduction to Solid State Physics or the study of physical properties of matter in a solid phase
Introduction to Solid State Physics or the study of physical properties of matter in a solid phase Prof. Germar Hoffmann 1. Crystal Structures 2. Reciprocal Lattice 3. Crystal Binding and Elastic Constants
More informationTHREE-DIMENSIONAL KINEMATICS OF RIGID BODIES
THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES 1. TRANSLATION Figure shows rigid body trnslting in three-dimensionl spce. Any two points in the body, such s A nd B, will move long prllel stright lines if
More informationStrategy: Use the Gibbs phase rule (Equation 5.3). How many components are present?
University Chemistry Quiz 4 2014/12/11 1. (5%) Wht is the dimensionlity of the three-phse coexistence region in mixture of Al, Ni, nd Cu? Wht type of geometricl region dose this define? Strtegy: Use the
More informationORBITAL DIAGRAM - A graphical representation of the quantum number "map" of electrons around an atom.
160 ORBITAL DIAGRAM - A graphical representation of the quantum number "map" of electrons around an atom. 4p 3d 4s 3p 3s 2p 2s 1s Each blank represents an ORBITAL, and can hold two electrons. The 4s subshell
More informationChapter 2. Vectors. 2.1 Vectors Scalars and Vectors
Chpter 2 Vectors 2.1 Vectors 2.1.1 Sclrs nd Vectors A vector is quntity hving both mgnitude nd direction. Emples of vector quntities re velocity, force nd position. One cn represent vector in n-dimensionl
More informationTHE SOLID STATE MODULE - 3 OBJECTIVES. Notes
The Solid Stte MODULE - 3 6 THE SOLID STATE You re wre tht the mtter exists in three different sttes viz., solid, liquid nd gs. In these, the constituent prticles (toms, molecules or ions) re held together
More informationThe Periodic Table of Elements
The Periodic Table of Elements 8 Uuo Uus Uuh (9) Uup (88) Uuq (89) Uut (8) Uub (8) Rg () 0 Ds (9) 09 Mt (8) 08 Hs (9) 0 h () 0 Sg () 0 Db () 0 Rf () 0 Lr () 88 Ra () 8 Fr () 8 Rn () 8 At (0) 8 Po (09)
More informationTopic 3: Periodicity OBJECTIVES FOR TODAY: Fall in love with the Periodic Table, Interpret trends in atomic radii, ionic radii, ionization energies &
Topic 3: Periodicity OBJECTIVES FOR TODAY: Fall in love with the Periodic Table, Interpret trends in atomic radii, ionic radii, ionization energies & electronegativity The Periodic Table What is the periodic
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
More informationFinite Automata. Informatics 2A: Lecture 3. John Longley. 22 September School of Informatics University of Edinburgh
Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 22 September 2017 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is
More informationChem 130 Second Exam
Nme Chem 130 Second Exm On the following pges you will find seven questions covering vries topics rnging from the structure of molecules, ions, nd solids to different models for explining bonding. Red
More informationChapter 3 Structures of Coordination Compounds
hpter 3 Structures of oordintion ompounds Problem Solutions: 3.1. Ethnol nd dimethylether re isomers becuse they hve the sme number nd types of toms but different properties. urthermore, they re structurl
More informationUNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences
UNIVERSITY OF OSLO Fculty of Mthemtics nd Nturl Sciences Midterm exm in MENA3100 Dy of exm: 19 th Mrch 2018 Exm hours: 14:30 17:30 This exmintion pper consists of 4 pges including 1 ppendix pge. Permitted
More information4 VECTORS. 4.0 Introduction. Objectives. Activity 1
4 VECTRS Chpter 4 Vectors jectives fter studying this chpter you should understnd the difference etween vectors nd sclrs; e le to find the mgnitude nd direction of vector; e le to dd vectors, nd multiply
More informationElement Cube Project (x2)
Element Cube Project (x2) Background: As a class, we will construct a three dimensional periodic table by each student selecting two elements in which you will need to create an element cube. Helpful Links
More informationShape and measurement
C H A P T E R 5 Shpe nd mesurement Wht is Pythgors theorem? How do we use Pythgors theorem? How do we find the perimeter of shpe? How do we find the re of shpe? How do we find the volume of shpe? How do
More informationCHEMICAL COMPOUNDS MOLECULAR COMPOUNDS
48 CHEMICAL COMPOUNDS - Dalton's theory does not mention this, but there is more than one way for atoms to come together to make chemical compounds! - There are TWO common kinds of chemical compound, classified
More informationSolutions and Ions. Pure Substances
Class #4 Solutions and Ions CHEM 107 L.S. Brown Texas A&M University Pure Substances Pure substance: described completely by a single chemical formula Fixed composition 1 Mixtures Combination of 2 or more
More informationamorphous solids, liquids and gases atoms or molecules are C A indentical and all properties are same in all directions.
THE SOLID STTE 1. INTRODUCTION : Mtter cn exist in three physicl sttes nmely ; solid, liquid nd gs. Mtter consists of tiny prticles (toms, ions or molecules). If the prticles re very fr off from one nother,
More informationReporting Category 1: Matter and Energy
Name: Science Teacher: Reporting Category 1: Matter and Energy Atoms Fill in the missing information to summarize what you know about atomic structure. Name of Subatomic Particle Location within the Atom
More informationmaterials and their properties
materials and their properties macroscopic properties phase state strength / stiffness electrical conductivity chemical properties color / transparence spectroscopical properties surface properties density
More informationBravais lattices and crystal systems
3 Brvis ltties nd rystl systems 3. Introdution The definitions of the motif, the repeting unit of pttern, nd the lttie, n rry of points in spe in whih eh point hs n identil environment, hold in three dimensions
More informationUniversity of Alabama Department of Physics and Astronomy. PH126: Exam 1
University of Albm Deprtment of Physics nd Astronomy PH 16 LeClir Fll 011 Instructions: PH16: Exm 1 1. Answer four of the five questions below. All problems hve equl weight.. You must show your work for
More informationTexture and Anisotroy. Part I: Chapter 2. Description of Orientation
Texture nd Anisotroy Prt I: Chter. Descrition of Orienttion Prt I: Fundmentl of Orienttion Orienttion mtrix Idel Orienttion Euler nles Anle/xis of rottion Rodriues vector Crystl systems Schemticlly, the
More informationLast 4 Digits of USC ID:
Chemistry 05 B Practice Exam Dr. Jessica Parr First Letter of last Name PLEASE PRINT YOUR NAME IN BLOCK LETTERS Name: Last 4 Digits of USC ID: Lab TA s Name: Question Points Score Grader 8 2 4 3 9 4 0
More informationDepartment of Electrical and Computer Engineering, Cornell University. ECE 4070: Physics of Semiconductors and Nanostructures.
Deprtment of Electricl nd Computer Engineering, Cornell University ECE 4070: Physics of Semiconductors nd Nnostructures Spring 2014 Exm 2 ` April 17, 2014 INSTRUCTIONS: Every problem must be done in the
More informationC. Bulutay Topics on Semiconductor Physics. In This Lecture: Electronic Bandstructure: General Info
C. Buluty Topics on Semiconductor Physics In This Lecture: Electronic Bndstructure: Generl Info C. Buluty Topics on Semiconductor Physics Electronic Bndstructure Acronyms FPLAPW: Full-potentil linerized
More informationReferences and Resources:
Surfce nd Interfce Science Physics 627; Chemistry 542 Lectures 4 Feb 3, 2013 Determining Surfce Structure Diffrction methods: LEED; RHEED Rel Spce: STEM References nd Resources: Woodruff nd Delchr (2 nd
More informationExample: Helium has an atomic number of 2. Every helium atom has two protons in its nucleus.
59 Atomic terms - ATOMIC NUMBER: The number of protons in the atomic nucleus. Each ELEMENT has the SAME NUMBER OF PROTONS in every nucleus. In neutral atoms, the number of ELECTRONS is also equal to the
More information-"l" also contributes ENERGY. Higher values for "l" mean the electron has higher energy.
170 - Giving the four parameters will uniquely identify an electron around an atom. No two electrons in the same atom can share all four. These parameters are called QUANTUM NUMBERS. PRINCIPAL QUANTUM
More informationMATRICES AND VECTORS SPACE
MATRICES AND VECTORS SPACE MATRICES AND MATRIX OPERATIONS SYSTEM OF LINEAR EQUATIONS DETERMINANTS VECTORS IN -SPACE AND -SPACE GENERAL VECTOR SPACES INNER PRODUCT SPACES EIGENVALUES, EIGENVECTORS LINEAR
More informationNucleus. Electron Cloud
Atomic Structure I. Picture of an Atom Nucleus Electron Cloud II. Subatomic particles Particle Symbol Charge Relative Mass (amu) protons p + +1 1.0073 neutrons n 0 1.0087 electrons e - -1 0.00054858 Compare
More informationElementary Linear Algebra
Elementry Liner Algebr Anton & Rorres, 1 th Edition Lecture Set 5 Chpter 4: Prt II Generl Vector Spces 163 คณ ตศาสตร ว ศวกรรม 3 สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา 1/2555 163 คณตศาสตรวศวกรรม 3 สาขาวชาวศวกรรมคอมพวเตอร
More informationAtomic weight: This is a decimal number, but for radioactive elements it is replaced with a number in parenthesis.
47 Blocks on the periodic table 11 Sodium 22.99 Atomic number: This is always a whole number. The periodic table is arranged by atomic number! Element symbol: A one or two letter abbreviation for the name
More informationMath 520 Final Exam Topic Outline Sections 1 3 (Xiao/Dumas/Liaw) Spring 2008
Mth 520 Finl Exm Topic Outline Sections 1 3 (Xio/Dums/Liw) Spring 2008 The finl exm will be held on Tuesdy, My 13, 2-5pm in 117 McMilln Wht will be covered The finl exm will cover the mteril from ll of
More informationNAME (please print) MIDTERM EXAM FIRST LAST JULY 13, 2011
CEMISTRY 140A NAME (please print) MIDTERM EXAM IRST LAST JULY 13, 2011 SIGNATURE Vollhardt & Schore 6 th Edition Cp. 1 through 5 ID NUMBER LAST NAME PERSN SEATED IN T YUR RIGT: LAST NAME PERSN SEATED T
More informationWRITING AN IONIC FORMULA
WRITING AN IONIC FORMULA - if you know the ions that make up a compound, all you need to do is find the smallest ratio of cation to anion the compound needs to have an overall charge of zero Example: If
More informationCHEM 10113, Quiz 5 October 26, 2011
CHEM 10113, Quiz 5 October 26, 2011 Name (please print) All equations must be balanced and show phases for full credit. Significant figures count, show charges as appropriate, and please box your answers!
More informationExample: If a simple ionic compound is made of these two ions, what is its formula? In the final formula, don't write the charges on the ions!
88 WRITING AN IONIC FORMULA - if you know the ions that make up a compound, all you need to do is find the smallest ratio of cation to anion the compound needs to have an overall charge of zero Example:
More informationProblem 3: Band Structure of YBa 2 Cu 3 O 7
HW 5 SSP 601-2017. here is very relistic clcultion which uses the concepts of lttice, reciprocl spce, Brillouin zone nd tight-binding pproximtion. Go over the solution nd fill up every step nd every detil
More informationII crystal structure
II crstal structure 2-1 basic concept > Crstal structure = lattice structure + basis > Lattice point: positions (points) in the structure which are identical. > Lattice translation vector > Lattice plane
More informationPERIODIC TABLE OF THE ELEMENTS
Useful Constants and equations: K = o C + 273 Avogadro's number = 6.022 x 10 23 d = density = mass/volume R H = 2.178 x 10-18 J c = E = h = hc/ h = 6.626 x 10-34 J s c = 2.998 x 10 8 m/s E n = -R H Z 2
More informationPart 2. Multiple choice (use answer card). 90 pts. total. 3 pts. each.
1 Exam I CHEM 1303.001 Name (print legibly) Seat no. On my honor, I have neither given nor received unauthorized aid on this exam. Signed Date Part 1. Nomenclature. 10 pts. total. 2 pts. each. Fill in
More information... but using electron configurations to describe how aluminum bromide forms is a bit cumbersome! Can we simplify the picture a bit?
193... but using electron configurations to describe how aluminum bromide forms is a bit cumbersome! Can we simplify the picture a bit? LEWIS NOTATION / ELECTRON-DOT NOTATION - Lewis notation represents
More informationLewis dot structures for molecules
1 Lewis dot structures for molecules In the dot structure of a molecule, - SHARED valence electrons are shown with dashes - one per pair. - UNSHARED valence electrons ("lone pairs") are represented by
More informationVIIIA H PREDICTING CHARGE
58 IA PREDICTING CHARGE VIIIA H IIA IIIA IVA VA VIA VIIA You can reliably determine the charge using our method for Groups IA, IIA, IIIB, Aluminum, and the Group VA, VIA, and VIIA NONMETALS Li Be B C N
More informationCrystallographic structure Physical vs Chemical bonding in solids
Crystallographic structure Physical vs Chemical bonding in solids Inert gas and molecular crystals: Van der Waals forces (physics) Water and organic chemistry H bonds (physics) Quartz crystal SiO 2 : covalent
More information13.3 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS
33 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS As simple ppliction of the results we hve obtined on lgebric extensions, nd in prticulr on the multiplictivity of extension degrees, we cn nswer (in
More informationAtomic weight: This is a decimal number, but for radioactive elements it is replaced with a number in parenthesis.
47 Blocks on the periodic table 11 Sodium 22.99 Atomic number: This is always a whole number. The periodic table is arranged by atomic number! Element symbol: A one or two letter abbreviation for the name
More informationChapter 3: Elements and Compounds. 3.1 Elements
Chapter 3: Elements and Compounds 3.1 Elements An element is a fundamental substance that cannot be broken down by chemical or physical methods to simpler substances. The 118 known elements are nature
More informationAtomic Structure & Interatomic Bonding
Atomic Structure & Interatomic Bonding Chapter Outline Review of Atomic Structure Atomic Bonding Atomic Structure Atoms are the smallest structural units of all solids, liquids & gases. Atom: The smallest
More informationarxiv: v1 [physics.ed-ph] 23 Jul 2013
A proper understnding of the Dvisson nd Germer experiments for undergrdute modern physics course Mstsugu Suzuki nd Itsuko S. Suzuki Deprtment of Physics, Stte University of New York t Binghmton, Binghmton
More informationCOPYRIGHTED MATERIAL. Crystals and crystal structures. 1.1 Crystal families and crystal systems
1 Crystls nd crystl structures Wht is crystl system? Wht re unit cells? Wht informtion is needed to specify crystl structure? Crystls re solids tht possess long-rnge order. The rrngement of the toms t
More informationE5 Lewis Acids and Bases: lab 2. Session two lab Parts 2B, 3, and 4. Session one lab Parts 1and 2A. Aquo Complex Ions
E5 Lewis Acids and Bases: lab 2 Session one lab Parts 1and 2A Session two lab Parts 2B, 3, and 4 Part 2B. Complexation, Structure and Periodicity Compare the reactivity of aquo complex ions containing
More informationMade the FIRST periodic table
Made the FIRST periodic table 1869 Mendeleev organized the periodic table based on the similar properties and relativities of certain elements Later, Henri Moseley organized the elements by increasing
More information2. VECTORS AND MATRICES IN 3 DIMENSIONS
2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the
More informationPeriodic Table. - Mendeleev was able to predict the properties of previously unknown elements using his "periodic law" Modern periodic table
74 Periodic Table - Mendeleev (1869): --- When atoms are arranged in order of their atomic weight, some of their chemical and physical properties repeat at regular intervals (periods) --- Some of the physical
More informationUnit 1 Part 2 Atomic Structure and The Periodic Table Introduction to the Periodic Table UNIT 1 ATOMIC STRUCTURE AND THE PERIODIC TABLE
UNIT 1 ATOMIC STRUCTURE AND THE PERIODIC TABLE PART 2 INTRODUCTION TO THE PERIODIC TABLE Contents 1. The Structure of the Periodic Table 2. Trends in the Periodic Table Key words: group, period, block,
More information